1. Field of the Invention
This invention relates to a damped dynamic vibration absorber and more particularly to a damped dynamic vibration absorber to attenuate the lateral vibration of a pump which in operation has either fixed rotational speeds or a range of rotational speeds.
2. Description of the Prior Art
Apparatus such as pumps experience certain disturbing forces during their operation. For example, an imbalance of the rotational elements may result in disturbing forces acting on the pump bearings. Also, as the pump impeller rotates within the pump volute, a broad band hydraulic disturbing force is generated having periodic components which, in the case of a pump, have frequencies proportional to the rotational speed of the pump impeller. If the pump installation has a natural or resonant frequency near the frequencies of the disturbing force, the pump can begin to vibrate with sufficient amplitude to either cause objectionable noise and vibration of the pump equipment or damage the pump equipment or damage the pump support structure, or all three of the preceding. In the case of a pump having a range of operating rotational velocities, the problem of vibrations is compounded where the pump has multiple resonant frequencies within the range of frequencies of the periodic disturbing force.
There are several known solutions to attempt to attenuate vibration of a pump. However, in many instances, these solutions are impractical, aesthetically displeasing or uneconomical. For example, one solution may be to build a structure around the pump apparatus to tie to the apparatus to prevent vibration. However, available space or cost constraints may prohibit the additional construction of support apparatus and ties. Also, vibration may be reduced by greatly increasing the mass of the pump. However, such a solution is often uneconomical.
This invention contemplates a provision of a damped dynamic vibration absorber, or a number of such absorbers secured to the pump apparatus and tuned to have a natural frequency and damping ratio sufficient to attenuate vibration of the pump apparatus throughout the operating range.
Tuned vibration absorbers are in principle well known. For example, U.S. Pat. No. 4,150,588 to Brewer, issued Apr. 24, 1979, teaches an undamped vibration absorber to attenuate vibrations of an exhaust fan having a single operating speed. In the problem addressed by Brewer, the fan had a resonant frequency near the operating speed. While the teachings of Brewer may be acceptable for an apparatus having a single operating speed, it is not applicable to attenuate vibration of an apparatus having an operating speed over a wide range with multiple resonant frequencies within the operating range. Furthermore, the apparatus as taught by Brewer is tuneable to a single frequency. It is not effective at other frequencies which would be desirable for an apparatus having a wide range of operating speeds. For example, it may be desirable to tune a vibration absorber to be effective at any one of the following:
a. A frequency of a disturbing force; PA1 b. A resonant frequency of the pump system; PA1 c. A frequency that attenuates the displacement within a frequency range; and PA1 d. Two resonant frequencies of the pump installation.
Theories for applying the above tuning techniques to mathematically modeled systems are generally known. For example, Den Hartog, Mechanical Vibration, Fourth Edition McGraw-Hill (1956) teaches a theory for tuning an absorber to a resonant frequency for a mathematically modeled single degree of freedom system. Lewis, F. M. "Extended Theory of the Viscous Vibration Damper", Journal of Applied Mechanics, ASME Transcripts, Volume 22, pages 377-382 (1955) teaches a theory for tuning an absorber for a multi-mass modeled system. For the theory of tuning an absorber to a lowest structural response in a frequency range with multiple resonances, the following article discusses the problems in terms of mathematically modeled systems: Kwak, B. M., et al "Optimum Design of Damped Vibration Absorber Over a Finite Frequency Range" AIAA Journal, Volume 13, page 540 (April 1975). Tuning to two resonant frequencies of a multi-resonance structure is theoretically described in McMunn, J. C. et al "Multi-Parameter Optimum in Linear Dynamical Systems" ASME, Design Engineering Vibration Conference, March 1969.
While the mathematical theory of vibration absorbers is generally well developed, in practice as noted by Brewer, there are many difficulties in designing and constructing a tuned vibration absorber for particular applications. Indeed, the problem is particularly highlighted in the case of a pump which is a multi-degree of freedom apparatus and has multi-resonances within an operating range.